LMFDB - Embedded newform 6019.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20802 q^{2} -2.87685 q^{3} +2.87536 q^{4} +1.19118 q^{5} +6.35214 q^{6} -0.105056 q^{7} -1.93280 q^{8} +5.27625 q^{9} +O(q^{10})$	\(q-2.20802 q^{2} -2.87685 q^{3} +2.87536 q^{4} +1.19118 q^{5} +6.35214 q^{6} -0.105056 q^{7} -1.93280 q^{8} +5.27625 q^{9} -2.63016 q^{10} +2.37185 q^{11} -8.27196 q^{12} -1.00000 q^{13} +0.231966 q^{14} -3.42685 q^{15} -1.48304 q^{16} +7.30297 q^{17} -11.6501 q^{18} -3.69849 q^{19} +3.42508 q^{20} +0.302230 q^{21} -5.23709 q^{22} +5.61104 q^{23} +5.56038 q^{24} -3.58108 q^{25} +2.20802 q^{26} -6.54841 q^{27} -0.302073 q^{28} +2.61763 q^{29} +7.56656 q^{30} +3.62118 q^{31} +7.14019 q^{32} -6.82345 q^{33} -16.1251 q^{34} -0.125141 q^{35} +15.1711 q^{36} -3.01688 q^{37} +8.16635 q^{38} +2.87685 q^{39} -2.30233 q^{40} +3.21696 q^{41} -0.667330 q^{42} +5.89126 q^{43} +6.81991 q^{44} +6.28498 q^{45} -12.3893 q^{46} -13.1541 q^{47} +4.26648 q^{48} -6.98896 q^{49} +7.90710 q^{50} -21.0095 q^{51} -2.87536 q^{52} -2.12400 q^{53} +14.4590 q^{54} +2.82531 q^{55} +0.203053 q^{56} +10.6400 q^{57} -5.77979 q^{58} +6.88019 q^{59} -9.85343 q^{60} -7.18991 q^{61} -7.99565 q^{62} -0.554301 q^{63} -12.7996 q^{64} -1.19118 q^{65} +15.0663 q^{66} -0.729638 q^{67} +20.9986 q^{68} -16.1421 q^{69} +0.276314 q^{70} -10.2562 q^{71} -10.1980 q^{72} -10.5443 q^{73} +6.66134 q^{74} +10.3022 q^{75} -10.6345 q^{76} -0.249177 q^{77} -6.35214 q^{78} -1.19588 q^{79} -1.76657 q^{80} +3.01003 q^{81} -7.10312 q^{82} -6.45589 q^{83} +0.869019 q^{84} +8.69918 q^{85} -13.0080 q^{86} -7.53053 q^{87} -4.58432 q^{88} -8.93028 q^{89} -13.8774 q^{90} +0.105056 q^{91} +16.1337 q^{92} -10.4176 q^{93} +29.0446 q^{94} -4.40559 q^{95} -20.5412 q^{96} -1.92287 q^{97} +15.4318 q^{98} +12.5145 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.20802	−1.56131	−0.780653	−	0.624964i	$-0.785113\pi$
$2$	−2.20802	−1.56131	−0.780653	+	0.624964i	$0.785113\pi$
$3$	−2.87685	−1.66095	−0.830474	−	0.557057i	$-0.811930\pi$
$3$	−2.87685	−1.66095	−0.830474	+	0.557057i	$0.811930\pi$
$4$	2.87536	1.43768
$5$	1.19118	0.532714	0.266357	−	0.963874i	$-0.414180\pi$
$5$	1.19118	0.532714	0.266357	+	0.963874i	$0.414180\pi$
$6$	6.35214	2.59325
$7$	−0.105056	−0.0397074	−0.0198537	−	0.999803i	$-0.506320\pi$
$7$	−0.105056	−0.0397074	−0.0198537	+	0.999803i	$0.506320\pi$
$8$	−1.93280	−0.683350
$9$	5.27625	1.75875
$10$	−2.63016	−0.831729
$11$	2.37185	0.715140	0.357570	−	0.933886i	$-0.383605\pi$
$11$	2.37185	0.715140	0.357570	+	0.933886i	$0.383605\pi$
$12$	−8.27196	−2.38791
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.231966	0.0619955
$15$	−3.42685	−0.884810
$16$	−1.48304	−0.370760
$17$	7.30297	1.77123	0.885615	−	0.464421i	$-0.153737\pi$
$17$	7.30297	1.77123	0.885615	+	0.464421i	$0.153737\pi$
$18$	−11.6501	−2.74595
$19$	−3.69849	−0.848492	−0.424246	−	0.905547i	$-0.639461\pi$
$19$	−3.69849	−0.848492	−0.424246	+	0.905547i	$0.639461\pi$
$20$	3.42508	0.765871
$21$	0.302230	0.0659520
$22$	−5.23709	−1.11655
$23$	5.61104	1.16998	0.584991	−	0.811040i	$-0.301098\pi$
$23$	5.61104	1.16998	0.584991	+	0.811040i	$0.301098\pi$
$24$	5.56038	1.13501
$25$	−3.58108	−0.716216
$26$	2.20802	0.433029
$27$	−6.54841	−1.26024
$28$	−0.302073	−0.0570865
$29$	2.61763	0.486082	0.243041	−	0.970016i	$-0.421855\pi$
$29$	2.61763	0.486082	0.243041	+	0.970016i	$0.421855\pi$
$30$	7.56656	1.38146
$31$	3.62118	0.650384	0.325192	−	0.945648i	$-0.394571\pi$
$31$	3.62118	0.650384	0.325192	+	0.945648i	$0.394571\pi$
$32$	7.14019	1.26222
$33$	−6.82345	−1.18781
$34$	−16.1251	−2.76543
$35$	−0.125141	−0.0211527
$36$	15.1711	2.52851
$37$	−3.01688	−0.495973	−0.247986	−	0.968764i	$-0.579769\pi$
$37$	−3.01688	−0.495973	−0.247986	+	0.968764i	$0.579769\pi$
$38$	8.16635	1.32476
$39$	2.87685	0.460664
$40$	−2.30233	−0.364030
$41$	3.21696	0.502405	0.251203	−	0.967935i	$-0.419174\pi$
$41$	3.21696	0.502405	0.251203	+	0.967935i	$0.419174\pi$
$42$	−0.667330	−0.102971
$43$	5.89126	0.898409	0.449205	−	0.893429i	$-0.351707\pi$
$43$	5.89126	0.898409	0.449205	+	0.893429i	$0.351707\pi$
$44$	6.81991	1.02814
$45$	6.28498	0.936910
$46$	−12.3893	−1.82670
$47$	−13.1541	−1.91872	−0.959362	−	0.282178i	$-0.908943\pi$
$47$	−13.1541	−1.91872	−0.959362	+	0.282178i	$0.908943\pi$
$48$	4.26648	0.615813
$49$	−6.98896	−0.998423
$50$	7.90710	1.11823
$51$	−21.0095	−2.94192
$52$	−2.87536	−0.398740
$53$	−2.12400	−0.291753	−0.145877	−	0.989303i	$-0.546600\pi$
$53$	−2.12400	−0.291753	−0.145877	+	0.989303i	$0.546600\pi$
$54$	14.4590	1.96762
$55$	2.82531	0.380965
$56$	0.203053	0.0271341
$57$	10.6400	1.40930
$58$	−5.77979	−0.758923
$59$	6.88019	0.895724	0.447862	−	0.894103i	$-0.352186\pi$
$59$	6.88019	0.895724	0.447862	+	0.894103i	$0.352186\pi$
$60$	−9.85343	−1.27207
$61$	−7.18991	−0.920574	−0.460287	−	0.887770i	$-0.652253\pi$
$61$	−7.18991	−0.920574	−0.460287	+	0.887770i	$0.652253\pi$
$62$	−7.99565	−1.01545
$63$	−0.554301	−0.0698354
$64$	−12.7996	−1.59995
$65$	−1.19118	−0.147748
$66$	15.0663	1.85454
$67$	−0.729638	−0.0891394	−0.0445697	−	0.999006i	$-0.514192\pi$
$67$	−0.729638	−0.0891394	−0.0445697	+	0.999006i	$0.514192\pi$
$68$	20.9986	2.54646
$69$	−16.1421	−1.94328
$70$	0.276314	0.0330258
$71$	−10.2562	−1.21719	−0.608595	−	0.793481i	$-0.708266\pi$
$71$	−10.2562	−1.21719	−0.608595	+	0.793481i	$0.708266\pi$
$72$	−10.1980	−1.20184
$73$	−10.5443	−1.23412	−0.617058	−	0.786918i	$-0.711676\pi$
$73$	−10.5443	−1.23412	−0.617058	+	0.786918i	$0.711676\pi$
$74$	6.66134	0.774366
$75$	10.3022	1.18960
$76$	−10.6345	−1.21986
$77$	−0.249177	−0.0283964
$78$	−6.35214	−0.719238
$79$	−1.19588	−0.134546	−0.0672732	−	0.997735i	$-0.521430\pi$
$79$	−1.19588	−0.134546	−0.0672732	+	0.997735i	$0.521430\pi$
$80$	−1.76657	−0.197509
$81$	3.01003	0.334448
$82$	−7.10312	−0.784409
$83$	−6.45589	−0.708626	−0.354313	−	0.935127i	$-0.615285\pi$
$83$	−6.45589	−0.708626	−0.354313	+	0.935127i	$0.615285\pi$
$84$	0.869019	0.0948177
$85$	8.69918	0.943558
$86$	−13.0080	−1.40269
$87$	−7.53053	−0.807357
$88$	−4.58432	−0.488691
$89$	−8.93028	−0.946608	−0.473304	−	0.880899i	$-0.656939\pi$
$89$	−8.93028	−0.946608	−0.473304	+	0.880899i	$0.656939\pi$
$90$	−13.8774	−1.46280
$91$	0.105056	0.0110129
$92$	16.1337	1.68206
$93$	−10.4176	−1.08025
$94$	29.0446	2.99572
$95$	−4.40559	−0.452003
$96$	−20.5412	−2.09648
$97$	−1.92287	−0.195238	−0.0976191	−	0.995224i	$-0.531123\pi$
$97$	−1.92287	−0.195238	−0.0976191	+	0.995224i	$0.531123\pi$
$98$	15.4318	1.55884
$99$	12.5145	1.25775
$100$	−10.2969	−1.02969
$101$	−17.5409	−1.74539	−0.872694	−	0.488268i	$-0.837629\pi$
$101$	−17.5409	−1.74539	−0.872694	+	0.488268i	$0.837629\pi$
$102$	46.3894	4.59324
$103$	18.8338	1.85575	0.927875	−	0.372890i	$-0.121633\pi$
$103$	18.8338	1.85575	0.927875	+	0.372890i	$0.121633\pi$
$104$	1.93280	0.189527
$105$	0.360012	0.0351335
$106$	4.68983	0.455517
$107$	8.51796	0.823462	0.411731	−	0.911305i	$-0.364924\pi$
$107$	8.51796	0.823462	0.411731	+	0.911305i	$0.364924\pi$
$108$	−18.8290	−1.81182
$109$	−20.0830	−1.92360	−0.961801	−	0.273751i	$-0.911736\pi$
$109$	−20.0830	−1.92360	−0.961801	+	0.273751i	$0.911736\pi$
$110$	−6.23834	−0.594803
$111$	8.67911	0.823785
$112$	0.155802	0.0147219
$113$	−0.599024	−0.0563514	−0.0281757	−	0.999603i	$-0.508970\pi$
$113$	−0.599024	−0.0563514	−0.0281757	+	0.999603i	$0.508970\pi$
$114$	−23.4933	−2.20035
$115$	6.68378	0.623265
$116$	7.52663	0.698830
$117$	−5.27625	−0.487789
$118$	−15.1916	−1.39850
$119$	−0.767220	−0.0703310
$120$	6.62344	0.604635
$121$	−5.37433	−0.488575
$122$	15.8755	1.43730
$123$	−9.25471	−0.834469
$124$	10.4122	0.935042
$125$	−10.2216	−0.914252
$126$	1.22391	0.109034
$127$	−4.09597	−0.363459	−0.181729	−	0.983349i	$-0.558169\pi$
$127$	−4.09597	−0.363459	−0.181729	+	0.983349i	$0.558169\pi$
$128$	13.9814	1.23580
$129$	−16.9483	−1.49221
$130$	2.63016	0.230680
$131$	17.5563	1.53390	0.766952	−	0.641705i	$-0.221773\pi$
$131$	17.5563	1.53390	0.766952	+	0.641705i	$0.221773\pi$
$132$	−19.6198	−1.70769
$133$	0.388549	0.0336914
$134$	1.61106	0.139174
$135$	−7.80036	−0.671348
$136$	−14.1152	−1.21037
$137$	7.88424	0.673596	0.336798	−	0.941577i	$-0.390656\pi$
$137$	7.88424	0.673596	0.336798	+	0.941577i	$0.390656\pi$
$138$	35.6421	3.03405
$139$	−6.14073	−0.520850	−0.260425	−	0.965494i	$-0.583863\pi$
$139$	−6.14073	−0.520850	−0.260425	+	0.965494i	$0.583863\pi$
$140$	−0.359825	−0.0304108
$141$	37.8424	3.18690
$142$	22.6459	1.90041
$143$	−2.37185	−0.198344
$144$	−7.82488	−0.652073
$145$	3.11808	0.258943
$146$	23.2820	1.92683
$147$	20.1062	1.65833
$148$	−8.67462	−0.713049
$149$	−11.1779	−0.915727	−0.457864	−	0.889022i	$-0.651385\pi$
$149$	−11.1779	−0.915727	−0.457864	+	0.889022i	$0.651385\pi$
$150$	−22.7475	−1.85733
$151$	−10.0591	−0.818598	−0.409299	−	0.912400i	$-0.634227\pi$
$151$	−10.0591	−0.818598	−0.409299	+	0.912400i	$0.634227\pi$
$152$	7.14846	0.579817
$153$	38.5322	3.11515
$154$	0.550188	0.0443354
$155$	4.31350	0.346468
$156$	8.27196	0.662287
$157$	2.21286	0.176606	0.0883029	−	0.996094i	$-0.471856\pi$
$157$	2.21286	0.176606	0.0883029	+	0.996094i	$0.471856\pi$
$158$	2.64052	0.210068
$159$	6.11041	0.484587
$160$	8.50528	0.672402
$161$	−0.589473	−0.0464570
$162$	−6.64622	−0.522176
$163$	−5.07204	−0.397273	−0.198637	−	0.980073i	$-0.563651\pi$
$163$	−5.07204	−0.397273	−0.198637	+	0.980073i	$0.563651\pi$
$164$	9.24992	0.722297
$165$	−8.12798	−0.632763
$166$	14.2547	1.10638
$167$	12.9061	0.998704	0.499352	−	0.866399i	$-0.333571\pi$
$167$	12.9061	0.998704	0.499352	+	0.866399i	$0.333571\pi$
$168$	−0.584151	−0.0450683
$169$	1.00000	0.0769231
$170$	−19.2080	−1.47318
$171$	−19.5142	−1.49228
$172$	16.9395	1.29162
$173$	−12.3925	−0.942186	−0.471093	−	0.882084i	$-0.656140\pi$
$173$	−12.3925	−0.942186	−0.471093	+	0.882084i	$0.656140\pi$
$174$	16.6276	1.26053
$175$	0.376214	0.0284391
$176$	−3.51755	−0.265145
$177$	−19.7932	−1.48775
$178$	19.7182	1.47794
$179$	9.96551	0.744857	0.372429	−	0.928061i	$-0.378525\pi$
$179$	9.96551	0.744857	0.372429	+	0.928061i	$0.378525\pi$
$180$	18.0716	1.34697
$181$	−11.2710	−0.837766	−0.418883	−	0.908040i	$-0.637578\pi$
$181$	−11.2710	−0.837766	−0.418883	+	0.908040i	$0.637578\pi$
$182$	−0.231966	−0.0171944
$183$	20.6843	1.52903
$184$	−10.8450	−0.799507
$185$	−3.59367	−0.264212
$186$	23.0023	1.68661
$187$	17.3215	1.26668
$188$	−37.8228	−2.75851
$189$	0.687950	0.0500410
$190$	9.72762	0.705716
$191$	−15.5242	−1.12329	−0.561646	−	0.827378i	$-0.689832\pi$
$191$	−15.5242	−1.12329	−0.561646	+	0.827378i	$0.689832\pi$
$192$	36.8225	2.65744
$193$	2.38822	0.171908	0.0859538	−	0.996299i	$-0.472606\pi$
$193$	2.38822	0.171908	0.0859538	+	0.996299i	$0.472606\pi$
$194$	4.24575	0.304827
$195$	3.42685	0.245402
$196$	−20.0958	−1.43541
$197$	8.53080	0.607794	0.303897	−	0.952705i	$-0.401712\pi$
$197$	8.53080	0.607794	0.303897	+	0.952705i	$0.401712\pi$
$198$	−27.6322	−1.96373
$199$	4.11082	0.291408	0.145704	−	0.989328i	$-0.453455\pi$
$199$	4.11082	0.291408	0.145704	+	0.989328i	$0.453455\pi$
$200$	6.92153	0.489426
$201$	2.09906	0.148056
$202$	38.7307	2.72509
$203$	−0.274998	−0.0193011
$204$	−60.4098	−4.22953
$205$	3.83200	0.267638
$206$	−41.5855	−2.89740
$207$	29.6052	2.05770
$208$	1.48304	0.102830
$209$	−8.77227	−0.606791
$210$	−0.794913	−0.0548542
$211$	24.8340	1.70964	0.854820	−	0.518925i	$-0.173668\pi$
$211$	24.8340	1.70964	0.854820	+	0.518925i	$0.173668\pi$
$212$	−6.10725	−0.419448
$213$	29.5056	2.02169
$214$	−18.8078	−1.28568
$215$	7.01758	0.478595
$216$	12.6568	0.861186
$217$	−0.380427	−0.0258251
$218$	44.3437	3.00333
$219$	30.3343	2.04980
$220$	8.12377	0.547705
$221$	−7.30297	−0.491251
$222$	−19.1637	−1.28618
$223$	21.1415	1.41574	0.707869	−	0.706344i	$-0.249657\pi$
$223$	21.1415	1.41574	0.707869	+	0.706344i	$0.249657\pi$
$224$	−0.750120	−0.0501195
$225$	−18.8947	−1.25964
$226$	1.32266	0.0879819
$227$	5.67892	0.376923	0.188462	−	0.982081i	$-0.439650\pi$
$227$	5.67892	0.376923	0.188462	+	0.982081i	$0.439650\pi$
$228$	30.5938	2.02612
$229$	−7.25286	−0.479282	−0.239641	−	0.970862i	$-0.577030\pi$
$229$	−7.25286	−0.479282	−0.239641	+	0.970862i	$0.577030\pi$
$230$	−14.7579	−0.973108
$231$	0.716844	0.0471649
$232$	−5.05937	−0.332164
$233$	0.139872	0.00916333	0.00458167	−	0.999990i	$-0.498542\pi$
$233$	0.139872	0.00916333	0.00458167	+	0.999990i	$0.498542\pi$
$234$	11.6501	0.761588
$235$	−15.6690	−1.02213
$236$	19.7830	1.28776
$237$	3.44035	0.223475
$238$	1.69404	0.109808
$239$	−17.4169	−1.12661	−0.563304	−	0.826250i	$-0.690470\pi$
$239$	−17.4169	−1.12661	−0.563304	+	0.826250i	$0.690470\pi$
$240$	5.08216	0.328052
$241$	8.16718	0.526094	0.263047	−	0.964783i	$-0.415273\pi$
$241$	8.16718	0.526094	0.263047	+	0.964783i	$0.415273\pi$
$242$	11.8666	0.762816
$243$	10.9858	0.704741
$244$	−20.6736	−1.32349
$245$	−8.32514	−0.531874
$246$	20.4346	1.30286
$247$	3.69849	0.235329
$248$	−6.99904	−0.444440
$249$	18.5726	1.17699
$250$	22.5696	1.42743
$251$	5.72186	0.361161	0.180580	−	0.983560i	$-0.442202\pi$
$251$	5.72186	0.361161	0.180580	+	0.983560i	$0.442202\pi$
$252$	−1.59381	−0.100401
$253$	13.3085	0.836700
$254$	9.04399	0.567471
$255$	−25.0262	−1.56720
$256$	−5.27206	−0.329504
$257$	−3.79970	−0.237019	−0.118510	−	0.992953i	$-0.537812\pi$
$257$	−3.79970	−0.237019	−0.118510	+	0.992953i	$0.537812\pi$
$258$	37.4221	2.32980
$259$	0.316942	0.0196938
$260$	−3.42508	−0.212414
$261$	13.8113	0.854896
$262$	−38.7647	−2.39489
$263$	−8.50785	−0.524617	−0.262308	−	0.964984i	$-0.584484\pi$
$263$	−8.50785	−0.524617	−0.262308	+	0.964984i	$0.584484\pi$
$264$	13.1884	0.811690
$265$	−2.53007	−0.155421
$266$	−0.857924	−0.0526027
$267$	25.6910	1.57227
$268$	−2.09797	−0.128154
$269$	−14.7218	−0.897604	−0.448802	−	0.893631i	$-0.648149\pi$
$269$	−14.7218	−0.897604	−0.448802	+	0.893631i	$0.648149\pi$
$270$	17.2234	1.04818
$271$	−19.3218	−1.17372	−0.586858	−	0.809690i	$-0.699636\pi$
$271$	−19.3218	−1.17372	−0.586858	+	0.809690i	$0.699636\pi$
$272$	−10.8306	−0.656701
$273$	−0.302230	−0.0182918
$274$	−17.4086	−1.05169
$275$	−8.49379	−0.512195
$276$	−46.4143	−2.79381
$277$	−16.0375	−0.963601	−0.481801	−	0.876281i	$-0.660017\pi$
$277$	−16.0375	−0.963601	−0.481801	+	0.876281i	$0.660017\pi$
$278$	13.5589	0.813207
$279$	19.1063	1.14386
$280$	0.241873	0.0144547
$281$	11.6575	0.695430	0.347715	−	0.937600i	$-0.386958\pi$
$281$	11.6575	0.695430	0.347715	+	0.937600i	$0.386958\pi$
$282$	−83.5567	−4.97573
$283$	9.85784	0.585988	0.292994	−	0.956114i	$-0.405348\pi$
$283$	9.85784	0.585988	0.292994	+	0.956114i	$0.405348\pi$
$284$	−29.4903	−1.74993
$285$	12.6742	0.750754
$286$	5.23709	0.309676
$287$	−0.337961	−0.0199492
$288$	37.6734	2.21993
$289$	36.3333	2.13725
$290$	−6.88479	−0.404289
$291$	5.53181	0.324281
$292$	−30.3186	−1.77426
$293$	11.0214	0.643878	0.321939	−	0.946760i	$-0.395665\pi$
$293$	11.0214	0.643878	0.321939	+	0.946760i	$0.395665\pi$
$294$	−44.3949	−2.58916
$295$	8.19557	0.477164
$296$	5.83105	0.338923
$297$	−15.5318	−0.901249
$298$	24.6810	1.42973
$299$	−5.61104	−0.324495
$300$	29.6225	1.71026
$301$	−0.618912	−0.0356735
$302$	22.2107	1.27808
$303$	50.4626	2.89900
$304$	5.48501	0.314587
$305$	−8.56451	−0.490402
$306$	−85.0800	−4.86370
$307$	10.7776	0.615108	0.307554	−	0.951531i	$-0.400490\pi$
$307$	10.7776	0.615108	0.307554	+	0.951531i	$0.400490\pi$
$308$	−0.716473	−0.0408248
$309$	−54.1820	−3.08231
$310$	−9.52429	−0.540943
$311$	5.26016	0.298276	0.149138	−	0.988816i	$-0.452350\pi$
$311$	5.26016	0.298276	0.149138	+	0.988816i	$0.452350\pi$
$312$	−5.56038	−0.314795
$313$	23.2185	1.31239	0.656193	−	0.754593i	$-0.272166\pi$
$313$	23.2185	1.31239	0.656193	+	0.754593i	$0.272166\pi$
$314$	−4.88605	−0.275736
$315$	−0.660275	−0.0372023
$316$	−3.43857	−0.193435
$317$	−30.0776	−1.68933	−0.844664	−	0.535297i	$-0.820200\pi$
$317$	−30.0776	−1.68933	−0.844664	+	0.535297i	$0.820200\pi$
$318$	−13.4919	−0.756589
$319$	6.20863	0.347617
$320$	−15.2467	−0.852316
$321$	−24.5049	−1.36773
$322$	1.30157	0.0725336
$323$	−27.0100	−1.50287
$324$	8.65492	0.480829
$325$	3.58108	0.198643
$326$	11.1992	0.620265
$327$	57.7757	3.19500
$328$	−6.21776	−0.343318
$329$	1.38192	0.0761876
$330$	17.9468	0.987937
$331$	7.74017	0.425438	0.212719	−	0.977113i	$-0.431768\pi$
$331$	7.74017	0.425438	0.212719	+	0.977113i	$0.431768\pi$
$332$	−18.5630	−1.01878
$333$	−15.9178	−0.872292
$334$	−28.4969	−1.55928
$335$	−0.869133	−0.0474858
$336$	−0.448219	−0.0244523
$337$	−9.43977	−0.514217	−0.257108	−	0.966383i	$-0.582770\pi$
$337$	−9.43977	−0.514217	−0.257108	+	0.966383i	$0.582770\pi$
$338$	−2.20802	−0.120101
$339$	1.72330	0.0935968
$340$	25.0132	1.35653
$341$	8.58890	0.465115
$342$	43.0877	2.32991
$343$	1.46962	0.0793523
$344$	−11.3867	−0.613928
$345$	−19.2282	−1.03521
$346$	27.3629	1.47104
$347$	−25.3195	−1.35922	−0.679611	−	0.733572i	$-0.737852\pi$
$347$	−25.3195	−1.35922	−0.679611	+	0.733572i	$0.737852\pi$
$348$	−21.6529	−1.16072
$349$	12.8013	0.685236	0.342618	−	0.939475i	$-0.388686\pi$
$349$	12.8013	0.685236	0.342618	+	0.939475i	$0.388686\pi$
$350$	−0.830688	−0.0444022
$351$	6.54841	0.349528
$352$	16.9355	0.902663
$353$	16.7519	0.891616	0.445808	−	0.895129i	$-0.352916\pi$
$353$	16.7519	0.891616	0.445808	+	0.895129i	$0.352916\pi$
$354$	43.7039	2.32284
$355$	−12.2170	−0.648413
$356$	−25.6777	−1.36092
$357$	2.20718	0.116816
$358$	−22.0041	−1.16295
$359$	−16.4037	−0.865752	−0.432876	−	0.901453i	$-0.642501\pi$
$359$	−16.4037	−0.865752	−0.432876	+	0.901453i	$0.642501\pi$
$360$	−12.1476	−0.640237
$361$	−5.32116	−0.280061
$362$	24.8866	1.30801
$363$	15.4611	0.811498
$364$	0.302073	0.0158329
$365$	−12.5602	−0.657431
$366$	−45.6713	−2.38728
$367$	−25.9556	−1.35487	−0.677435	−	0.735583i	$-0.736908\pi$
$367$	−25.9556	−1.35487	−0.677435	+	0.735583i	$0.736908\pi$
$368$	−8.32139	−0.433782
$369$	16.9735	0.883605
$370$	7.93489	0.412515
$371$	0.223139	0.0115848
$372$	−29.9543	−1.55306
$373$	4.11030	0.212823	0.106412	−	0.994322i	$-0.466064\pi$
$373$	4.11030	0.212823	0.106412	+	0.994322i	$0.466064\pi$
$374$	−38.2463	−1.97767
$375$	29.4061	1.51852
$376$	25.4243	1.31116
$377$	−2.61763	−0.134815
$378$	−1.51901	−0.0781293
$379$	13.3468	0.685578	0.342789	−	0.939412i	$-0.388628\pi$
$379$	13.3468	0.685578	0.342789	+	0.939412i	$0.388628\pi$
$380$	−12.6676	−0.649836
$381$	11.7835	0.603686
$382$	34.2778	1.75380
$383$	−2.69363	−0.137638	−0.0688191	−	0.997629i	$-0.521923\pi$
$383$	−2.69363	−0.137638	−0.0688191	+	0.997629i	$0.521923\pi$
$384$	−40.2224	−2.05259
$385$	−0.296816	−0.0151271
$386$	−5.27323	−0.268401
$387$	31.0838	1.58008
$388$	−5.52895	−0.280690
$389$	23.1966	1.17611	0.588056	−	0.808820i	$-0.299893\pi$
$389$	23.1966	1.17611	0.588056	+	0.808820i	$0.299893\pi$
$390$	−7.56656	−0.383148
$391$	40.9772	2.07231
$392$	13.5083	0.682272
$393$	−50.5068	−2.54773
$394$	−18.8362	−0.948953
$395$	−1.42451	−0.0716748
$396$	35.9835	1.80824
$397$	−10.2639	−0.515130	−0.257565	−	0.966261i	$-0.582920\pi$
$397$	−10.2639	−0.515130	−0.257565	+	0.966261i	$0.582920\pi$
$398$	−9.07677	−0.454977
$399$	−1.11780	−0.0559597
$400$	5.31088	0.265544
$401$	5.67332	0.283312	0.141656	−	0.989916i	$-0.454757\pi$
$401$	5.67332	0.283312	0.141656	+	0.989916i	$0.454757\pi$
$402$	−4.63476	−0.231161
$403$	−3.62118	−0.180384
$404$	−50.4364	−2.50931
$405$	3.58550	0.178165
$406$	0.607201	0.0301349
$407$	−7.15560	−0.354690
$408$	40.6073	2.01036
$409$	18.4101	0.910322	0.455161	−	0.890409i	$-0.349582\pi$
$409$	18.4101	0.910322	0.455161	+	0.890409i	$0.349582\pi$
$410$	−8.46113	−0.417865
$411$	−22.6818	−1.11881
$412$	54.1539	2.66797
$413$	−0.722805	−0.0355669
$414$	−65.3689	−3.21271
$415$	−7.69016	−0.377495
$416$	−7.14019	−0.350077
$417$	17.6659	0.865105
$418$	19.3694	0.947386
$419$	−13.9312	−0.680581	−0.340291	−	0.940320i	$-0.610525\pi$
$419$	−13.9312	−0.680581	−0.340291	+	0.940320i	$0.610525\pi$
$420$	1.03516	0.0505107
$421$	−14.3201	−0.697918	−0.348959	−	0.937138i	$-0.613465\pi$
$421$	−14.3201	−0.697918	−0.348959	+	0.937138i	$0.613465\pi$
$422$	−54.8339	−2.66927
$423$	−69.4043	−3.37455
$424$	4.10527	0.199370
$425$	−26.1525	−1.26858
$426$	−65.1489	−3.15647
$427$	0.755343	0.0365536
$428$	24.4922	1.18387
$429$	6.82345	0.329439
$430$	−15.4950	−0.747233
$431$	2.54093	0.122392	0.0611961	−	0.998126i	$-0.480509\pi$
$431$	2.54093	0.122392	0.0611961	+	0.998126i	$0.480509\pi$
$432$	9.71155	0.467247
$433$	4.33547	0.208349	0.104175	−	0.994559i	$-0.466780\pi$
$433$	4.33547	0.208349	0.104175	+	0.994559i	$0.466780\pi$
$434$	0.839991	0.0403208
$435$	−8.97024	−0.430090
$436$	−57.7457	−2.76552
$437$	−20.7524	−0.992720
$438$	−66.9788	−3.20037
$439$	−2.47639	−0.118192	−0.0590958	−	0.998252i	$-0.518822\pi$
$439$	−2.47639	−0.118192	−0.0590958	+	0.998252i	$0.518822\pi$
$440$	−5.46077	−0.260332
$441$	−36.8755	−1.75598
$442$	16.1251	0.766993
$443$	−30.8902	−1.46764	−0.733819	−	0.679345i	$-0.762264\pi$
$443$	−30.8902	−1.46764	−0.733819	+	0.679345i	$0.762264\pi$
$444$	24.9555	1.18434
$445$	−10.6376	−0.504271
$446$	−46.6808	−2.21040
$447$	32.1570	1.52098
$448$	1.34468	0.0635300
$449$	−8.75400	−0.413127	−0.206563	−	0.978433i	$-0.566228\pi$
$449$	−8.75400	−0.413127	−0.206563	+	0.978433i	$0.566228\pi$
$450$	41.7198	1.96669
$451$	7.63016	0.359290
$452$	−1.72241	−0.0810152
$453$	28.9385	1.35965
$454$	−12.5392	−0.588492
$455$	0.125141	0.00586670
$456$	−20.5650	−0.963046
$457$	28.6748	1.34135	0.670676	−	0.741750i	$-0.266004\pi$
$457$	28.6748	1.34135	0.670676	+	0.741750i	$0.266004\pi$
$458$	16.0145	0.748307
$459$	−47.8228	−2.23218
$460$	19.2182	0.896055
$461$	−12.8012	−0.596211	−0.298106	−	0.954533i	$-0.596355\pi$
$461$	−12.8012	−0.596211	−0.298106	+	0.954533i	$0.596355\pi$
$462$	−1.58281	−0.0736388
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−3.88205	−0.180220
$465$	−12.4093	−0.575466
$466$	−0.308841	−0.0143068
$467$	−28.4466	−1.31635	−0.658176	−	0.752864i	$-0.728672\pi$
$467$	−28.4466	−1.31635	−0.658176	+	0.752864i	$0.728672\pi$
$468$	−15.1711	−0.701284
$469$	0.0766528	0.00353950
$470$	34.5974	1.59586
$471$	−6.36607	−0.293333
$472$	−13.2981	−0.612093
$473$	13.9732	0.642488
$474$	−7.59636	−0.348913
$475$	13.2446	0.607704
$476$	−2.20603	−0.101113
$477$	−11.2067	−0.513121
$478$	38.4569	1.75898
$479$	−3.10569	−0.141903	−0.0709514	−	0.997480i	$-0.522604\pi$
$479$	−3.10569	−0.141903	−0.0709514	+	0.997480i	$0.522604\pi$
$480$	−24.4684	−1.11682
$481$	3.01688	0.137558
$482$	−18.0333	−0.821394
$483$	1.69582	0.0771626
$484$	−15.4531	−0.702414
$485$	−2.29050	−0.104006
$486$	−24.2569	−1.10032
$487$	−16.5352	−0.749280	−0.374640	−	0.927170i	$-0.622234\pi$
$487$	−16.5352	−0.749280	−0.374640	+	0.927170i	$0.622234\pi$
$488$	13.8967	0.629074
$489$	14.5915	0.659850
$490$	18.3821	0.830418
$491$	−39.3034	−1.77374	−0.886868	−	0.462023i	$-0.847124\pi$
$491$	−39.3034	−1.77374	−0.886868	+	0.462023i	$0.847124\pi$
$492$	−26.6106	−1.19970
$493$	19.1165	0.860963
$494$	−8.16635	−0.367421
$495$	14.9070	0.670021
$496$	−5.37036	−0.241136
$497$	1.07748	0.0483315
$498$	−41.0087	−1.83764
$499$	−3.66199	−0.163933	−0.0819667	−	0.996635i	$-0.526120\pi$
$499$	−3.66199	−0.163933	−0.0819667	+	0.996635i	$0.526120\pi$
$500$	−29.3909	−1.31440
$501$	−37.1289	−1.65880
$502$	−12.6340	−0.563883
$503$	8.07262	0.359940	0.179970	−	0.983672i	$-0.442400\pi$
$503$	8.07262	0.359940	0.179970	+	0.983672i	$0.442400\pi$
$504$	1.07136	0.0477220
$505$	−20.8945	−0.929792
$506$	−29.3855	−1.30635
$507$	−2.87685	−0.127765
$508$	−11.7774	−0.522537
$509$	13.7353	0.608809	0.304404	−	0.952543i	$-0.401543\pi$
$509$	13.7353	0.608809	0.304404	+	0.952543i	$0.401543\pi$
$510$	55.2584	2.44688
$511$	1.10774	0.0490036
$512$	−16.3220	−0.721339
$513$	24.2192	1.06931
$514$	8.38983	0.370059
$515$	22.4345	0.988584
$516$	−48.7323	−2.14532
$517$	−31.1996	−1.37216
$518$	−0.699814	−0.0307481
$519$	35.6514	1.56492
$520$	2.30233	0.100964
$521$	37.0344	1.62251	0.811254	−	0.584694i	$-0.198785\pi$
$521$	37.0344	1.62251	0.811254	+	0.584694i	$0.198785\pi$
$522$	−30.4956	−1.33476
$523$	−8.55393	−0.374037	−0.187019	−	0.982356i	$-0.559882\pi$
$523$	−8.55393	−0.374037	−0.187019	+	0.982356i	$0.559882\pi$
$524$	50.4807	2.20526
$525$	−1.08231	−0.0472359
$526$	18.7855	0.819088
$527$	26.4454	1.15198
$528$	10.1194	0.440392
$529$	8.48372	0.368857
$530$	5.58645	0.242660
$531$	36.3015	1.57535
$532$	1.11722	0.0484375
$533$	−3.21696	−0.139342
$534$	−56.7264	−2.45479
$535$	10.1465	0.438670
$536$	1.41025	0.0609134
$537$	−28.6692	−1.23717
$538$	32.5061	1.40144
$539$	−16.5768	−0.714012
$540$	−22.4288	−0.965183
$541$	−29.5839	−1.27191	−0.635956	−	0.771725i	$-0.719394\pi$
$541$	−29.5839	−1.27191	−0.635956	+	0.771725i	$0.719394\pi$
$542$	42.6630	1.83253
$543$	32.4249	1.39149
$544$	52.1446	2.23568
$545$	−23.9225	−1.02473
$546$	0.667330	0.0285591
$547$	−38.3344	−1.63906	−0.819531	−	0.573035i	$-0.805766\pi$
$547$	−38.3344	−1.63906	−0.819531	+	0.573035i	$0.805766\pi$
$548$	22.6700	0.968414
$549$	−37.9357	−1.61906
$550$	18.7545	0.799693
$551$	−9.68129	−0.412437
$552$	31.1995	1.32794
$553$	0.125634	0.00534250
$554$	35.4112	1.50448
$555$	10.3384	0.438842
$556$	−17.6568	−0.748815
$557$	24.9809	1.05847	0.529237	−	0.848474i	$-0.322478\pi$
$557$	24.9809	1.05847	0.529237	+	0.848474i	$0.322478\pi$
$558$	−42.1870	−1.78592
$559$	−5.89126	−0.249174
$560$	0.185589	0.00784257
$561$	−49.8314	−2.10388
$562$	−25.7401	−1.08578
$563$	−39.2329	−1.65347	−0.826735	−	0.562592i	$-0.809804\pi$
$563$	−39.2329	−1.65347	−0.826735	+	0.562592i	$0.809804\pi$
$564$	108.810	4.58174
$565$	−0.713548	−0.0300192
$566$	−21.7663	−0.914907
$567$	−0.316222	−0.0132801
$568$	19.8233	0.831766
$569$	−6.80393	−0.285236	−0.142618	−	0.989778i	$-0.545552\pi$
$569$	−6.80393	−0.285236	−0.142618	+	0.989778i	$0.545552\pi$
$570$	−27.9849	−1.17216
$571$	−37.3818	−1.56438	−0.782191	−	0.623039i	$-0.785898\pi$
$571$	−37.3818	−1.56438	−0.782191	+	0.623039i	$0.785898\pi$
$572$	−6.81991	−0.285155
$573$	44.6607	1.86573
$574$	0.746226	0.0311469
$575$	−20.0936	−0.837960
$576$	−67.5339	−2.81391
$577$	−13.2988	−0.553634	−0.276817	−	0.960923i	$-0.589280\pi$
$577$	−13.2988	−0.553634	−0.276817	+	0.960923i	$0.589280\pi$
$578$	−80.2247	−3.33691
$579$	−6.87053	−0.285530
$580$	8.96560	0.372276
$581$	0.678230	0.0281377
$582$	−12.2144	−0.506302
$583$	−5.03780	−0.208644
$584$	20.3801	0.843333
$585$	−6.28498	−0.259852
$586$	−24.3355	−1.00529
$587$	−4.35097	−0.179584	−0.0897918	−	0.995961i	$-0.528620\pi$
$587$	−4.35097	−0.179584	−0.0897918	+	0.995961i	$0.528620\pi$
$588$	57.8124	2.38414
$589$	−13.3929	−0.551846
$590$	−18.0960	−0.745000
$591$	−24.5418	−1.00951
$592$	4.47416	0.183887
$593$	32.1475	1.32014	0.660071	−	0.751204i	$-0.270526\pi$
$593$	32.1475	1.32014	0.660071	+	0.751204i	$0.270526\pi$
$594$	34.2946	1.40713
$595$	−0.913901	−0.0374663
$596$	−32.1404	−1.31652
$597$	−11.8262	−0.484014
$598$	12.3893	0.506635
$599$	47.8640	1.95567	0.977834	−	0.209381i	$-0.0671449\pi$
$599$	47.8640	1.95567	0.977834	+	0.209381i	$0.0671449\pi$
$600$	−19.9122	−0.812911
$601$	−17.4243	−0.710752	−0.355376	−	0.934723i	$-0.615647\pi$
$601$	−17.4243	−0.710752	−0.355376	+	0.934723i	$0.615647\pi$
$602$	1.36657	0.0556973
$603$	−3.84975	−0.156774
$604$	−28.9235	−1.17688
$605$	−6.40181	−0.260271
$606$	−111.422	−4.52623
$607$	−18.7018	−0.759082	−0.379541	−	0.925175i	$-0.623918\pi$
$607$	−18.7018	−0.759082	−0.379541	+	0.925175i	$0.623918\pi$
$608$	−26.4079	−1.07098
$609$	0.791127	0.0320581
$610$	18.9106	0.765668
$611$	13.1541	0.532158
$612$	110.794	4.47858
$613$	−31.8360	−1.28584	−0.642922	−	0.765932i	$-0.722278\pi$
$613$	−31.8360	−1.28584	−0.642922	+	0.765932i	$0.722278\pi$
$614$	−23.7971	−0.960372
$615$	−11.0241	−0.444533
$616$	0.481611	0.0194046
$617$	4.24549	0.170917	0.0854584	−	0.996342i	$-0.472765\pi$
$617$	4.24549	0.170917	0.0854584	+	0.996342i	$0.472765\pi$
$618$	119.635	4.81242
$619$	−1.45326	−0.0584113	−0.0292056	−	0.999573i	$-0.509298\pi$
$619$	−1.45326	−0.0584113	−0.0292056	+	0.999573i	$0.509298\pi$
$620$	12.4028	0.498110
$621$	−36.7434	−1.47446
$622$	−11.6145	−0.465701
$623$	0.938179	0.0375874
$624$	−4.26648	−0.170796
$625$	5.72954	0.229182
$626$	−51.2669	−2.04904
$627$	25.2365	1.00785
$628$	6.36277	0.253902
$629$	−22.0322	−0.878482
$630$	1.45790	0.0580841
$631$	−3.33568	−0.132791	−0.0663957	−	0.997793i	$-0.521150\pi$
$631$	−3.33568	−0.132791	−0.0663957	+	0.997793i	$0.521150\pi$
$632$	2.31139	0.0919423
$633$	−71.4435	−2.83962
$634$	66.4120	2.63756
$635$	−4.87906	−0.193620
$636$	17.5696	0.696681
$637$	6.98896	0.276913
$638$	−13.7088	−0.542736
$639$	−54.1143	−2.14073
$640$	16.6545	0.658325
$641$	42.1391	1.66439	0.832197	−	0.554480i	$-0.187083\pi$
$641$	42.1391	1.66439	0.832197	+	0.554480i	$0.187083\pi$
$642$	54.1072	2.13544
$643$	16.7637	0.661097	0.330549	−	0.943789i	$-0.392766\pi$
$643$	16.7637	0.661097	0.330549	+	0.943789i	$0.392766\pi$
$644$	−1.69494	−0.0667902
$645$	−20.1885	−0.794921
$646$	59.6386	2.34645
$647$	18.9527	0.745107	0.372554	−	0.928011i	$-0.378482\pi$
$647$	18.9527	0.745107	0.372554	+	0.928011i	$0.378482\pi$
$648$	−5.81781	−0.228545
$649$	16.3188	0.640568
$650$	−7.90710	−0.310142
$651$	1.09443	0.0428941
$652$	−14.5839	−0.571151
$653$	38.0324	1.48832	0.744162	−	0.667999i	$-0.232849\pi$
$653$	38.0324	1.48832	0.744162	+	0.667999i	$0.232849\pi$
$654$	−127.570	−4.98838
$655$	20.9128	0.817131
$656$	−4.77088	−0.186272
$657$	−55.6343	−2.17050
$658$	−3.05130	−0.118952
$659$	−22.1117	−0.861348	−0.430674	−	0.902508i	$-0.641724\pi$
$659$	−22.1117	−0.861348	−0.430674	+	0.902508i	$0.641724\pi$
$660$	−23.3708	−0.909709
$661$	−30.8942	−1.20164	−0.600822	−	0.799383i	$-0.705160\pi$
$661$	−30.8942	−1.20164	−0.600822	+	0.799383i	$0.705160\pi$
$662$	−17.0904	−0.664239
$663$	21.0095	0.815942
$664$	12.4780	0.484239
$665$	0.462833	0.0179479
$666$	35.1469	1.36191
$667$	14.6876	0.568707
$668$	37.1096	1.43582
$669$	−60.8208	−2.35147
$670$	1.91906	0.0741399
$671$	−17.0534	−0.658339
$672$	2.15798	0.0832459
$673$	−13.2849	−0.512096	−0.256048	−	0.966664i	$-0.582421\pi$
$673$	−13.2849	−0.512096	−0.256048	+	0.966664i	$0.582421\pi$
$674$	20.8432	0.802850
$675$	23.4504	0.902606
$676$	2.87536	0.110591
$677$	26.6469	1.02413	0.512063	−	0.858948i	$-0.328882\pi$
$677$	26.6469	1.02413	0.512063	+	0.858948i	$0.328882\pi$
$678$	−3.80508	−0.146133
$679$	0.202009	0.00775241
$680$	−16.8138	−0.644780
$681$	−16.3374	−0.626050
$682$	−18.9645	−0.726188
$683$	2.34275	0.0896430	0.0448215	−	0.998995i	$-0.485728\pi$
$683$	2.34275	0.0896430	0.0448215	+	0.998995i	$0.485728\pi$
$684$	−56.1101	−2.14542
$685$	9.39158	0.358834
$686$	−3.24496	−0.123893
$687$	20.8654	0.796063
$688$	−8.73697	−0.333094
$689$	2.12400	0.0809178
$690$	42.4563	1.61628
$691$	−35.5208	−1.35127	−0.675637	−	0.737234i	$-0.736132\pi$
$691$	−35.5208	−1.35127	−0.675637	+	0.737234i	$0.736132\pi$
$692$	−35.6329	−1.35456
$693$	−1.31472	−0.0499421
$694$	55.9060	2.12216
$695$	−7.31474	−0.277464
$696$	14.5550	0.551707
$697$	23.4934	0.889875
$698$	−28.2655	−1.06986
$699$	−0.402391	−0.0152198
$700$	1.08175	0.0408863
$701$	−37.1930	−1.40476	−0.702379	−	0.711803i	$-0.747879\pi$
$701$	−37.1930	−1.40476	−0.702379	+	0.711803i	$0.747879\pi$
$702$	−14.4590	−0.545721
$703$	11.1579	0.420829
$704$	−30.3588	−1.14419
$705$	45.0772	1.69771
$706$	−36.9886	−1.39209
$707$	1.84278	0.0693049
$708$	−56.9126	−2.13891
$709$	16.5083	0.619984	0.309992	−	0.950739i	$-0.399674\pi$
$709$	16.5083	0.619984	0.309992	+	0.950739i	$0.399674\pi$
$710$	26.9755	1.01237
$711$	−6.30973	−0.236633
$712$	17.2605	0.646864
$713$	20.3186	0.760937
$714$	−4.87349	−0.182386
$715$	−2.82531	−0.105661
$716$	28.6544	1.07086
$717$	50.1058	1.87124
$718$	36.2196	1.35170
$719$	19.2968	0.719649	0.359824	−	0.933020i	$-0.382837\pi$
$719$	19.2968	0.719649	0.359824	+	0.933020i	$0.382837\pi$
$720$	−9.32087	−0.347368
$721$	−1.97860	−0.0736871
$722$	11.7492	0.437261
$723$	−23.4957	−0.873815
$724$	−32.4081	−1.20444
$725$	−9.37395	−0.348140
$726$	−34.1385	−1.26700
$727$	45.0506	1.67083	0.835416	−	0.549618i	$-0.185227\pi$
$727$	45.0506	1.67083	0.835416	+	0.549618i	$0.185227\pi$
$728$	−0.203053	−0.00752563
$729$	−40.6346	−1.50499
$730$	27.7332	1.02645
$731$	43.0237	1.59129
$732$	59.4746	2.19825
$733$	−41.6143	−1.53706	−0.768529	−	0.639814i	$-0.779011\pi$
$733$	−41.6143	−1.53706	−0.768529	+	0.639814i	$0.779011\pi$
$734$	57.3104	2.11537
$735$	23.9502	0.883415
$736$	40.0639	1.47677
$737$	−1.73059	−0.0637471
$738$	−37.4778	−1.37958
$739$	34.8487	1.28193	0.640965	−	0.767570i	$-0.278534\pi$
$739$	34.8487	1.28193	0.640965	+	0.767570i	$0.278534\pi$
$740$	−10.3331	−0.379851
$741$	−10.6400	−0.390870
$742$	−0.492695	−0.0180874
$743$	−0.0612267	−0.00224619	−0.00112309	−	0.999999i	$-0.500357\pi$
$743$	−0.0612267	−0.00224619	−0.00112309	+	0.999999i	$0.500357\pi$
$744$	20.1352	0.738191
$745$	−13.3149	−0.487820
$746$	−9.07563	−0.332282
$747$	−34.0629	−1.24630
$748$	49.8056	1.82107
$749$	−0.894862	−0.0326976
$750$	−64.9293	−2.37088
$751$	−38.1465	−1.39199	−0.695993	−	0.718048i	$-0.745036\pi$
$751$	−38.1465	−1.39199	−0.695993	+	0.718048i	$0.745036\pi$
$752$	19.5081	0.711386
$753$	−16.4609	−0.599869
$754$	5.77979	0.210487
$755$	−11.9822	−0.436079
$756$	1.97810	0.0719428
$757$	7.44865	0.270726	0.135363	−	0.990796i	$-0.456780\pi$
$757$	7.44865	0.270726	0.135363	+	0.990796i	$0.456780\pi$
$758$	−29.4700	−1.07040
$759$	−38.2866	−1.38972
$760$	8.51514	0.308876
$761$	−3.17691	−0.115163	−0.0575814	−	0.998341i	$-0.518339\pi$
$761$	−3.17691	−0.115163	−0.0575814	+	0.998341i	$0.518339\pi$
$762$	−26.0182	−0.942539
$763$	2.10984	0.0763813
$764$	−44.6376	−1.61493
$765$	45.8990	1.65948
$766$	5.94760	0.214896
$767$	−6.88019	−0.248429
$768$	15.1669	0.547289
$769$	−17.3781	−0.626672	−0.313336	−	0.949642i	$-0.601447\pi$
$769$	−17.3781	−0.626672	−0.313336	+	0.949642i	$0.601447\pi$
$770$	0.655375	0.0236181
$771$	10.9312	0.393676
$772$	6.86698	0.247148
$773$	−5.90403	−0.212353	−0.106177	−	0.994347i	$-0.533861\pi$
$773$	−5.90403	−0.212353	−0.106177	+	0.994347i	$0.533861\pi$
$774$	−68.6336	−2.46698
$775$	−12.9677	−0.465815
$776$	3.71654	0.133416
$777$	−0.911793	−0.0327104
$778$	−51.2185	−1.83627
$779$	−11.8979	−0.426287
$780$	9.85343	0.352809
$781$	−24.3262	−0.870460
$782$	−90.4785	−3.23551
$783$	−17.1413	−0.612581
$784$	10.3649	0.370175
$785$	2.63593	0.0940803
$786$	111.520	3.97779
$787$	37.3092	1.32993	0.664965	−	0.746874i	$-0.268446\pi$
$787$	37.3092	1.32993	0.664965	+	0.746874i	$0.268446\pi$
$788$	24.5291	0.873813
$789$	24.4758	0.871361
$790$	3.14534	0.111906
$791$	0.0629311	0.00223757
$792$	−24.1880	−0.859484
$793$	7.18991	0.255321
$794$	22.6629	0.804275
$795$	7.27863	0.258146
$796$	11.8201	0.418951
$797$	−40.2900	−1.42714	−0.713572	−	0.700581i	$-0.752924\pi$
$797$	−40.2900	−1.42714	−0.713572	+	0.700581i	$0.752924\pi$
$798$	2.46811	0.0873703
$799$	−96.0640	−3.39850
$800$	−25.5696	−0.904022
$801$	−47.1184	−1.66485
$802$	−12.5268	−0.442337
$803$	−25.0095	−0.882565
$804$	6.03553	0.212857
$805$	−0.702171	−0.0247483
$806$	7.99565	0.281635
$807$	42.3524	1.49087
$808$	33.9032	1.19271
$809$	−22.9719	−0.807650	−0.403825	−	0.914836i	$-0.632320\pi$
$809$	−22.9719	−0.807650	−0.403825	+	0.914836i	$0.632320\pi$
$810$	−7.91687	−0.278170
$811$	0.123119	0.00432331	0.00216165	−	0.999998i	$-0.499312\pi$
$811$	0.123119	0.00432331	0.00216165	+	0.999998i	$0.499312\pi$
$812$	−0.790717	−0.0277487
$813$	55.5859	1.94948
$814$	15.7997	0.553780
$815$	−6.04174	−0.211633
$816$	31.1579	1.09075
$817$	−21.7888	−0.762293
$818$	−40.6499	−1.42129
$819$	0.554301	0.0193689
$820$	11.0184	0.384778
$821$	−43.9441	−1.53366	−0.766830	−	0.641850i	$-0.778167\pi$
$821$	−43.9441	−1.53366	−0.766830	+	0.641850i	$0.778167\pi$
$822$	50.0818	1.74680
$823$	33.3738	1.16334	0.581669	−	0.813426i	$-0.302400\pi$
$823$	33.3738	1.16334	0.581669	+	0.813426i	$0.302400\pi$
$824$	−36.4021	−1.26813
$825$	24.4353	0.850729
$826$	1.59597	0.0555308
$827$	16.3648	0.569060	0.284530	−	0.958667i	$-0.408162\pi$
$827$	16.3648	0.569060	0.284530	+	0.958667i	$0.408162\pi$
$828$	85.1255	2.95832
$829$	28.0757	0.975110	0.487555	−	0.873092i	$-0.337889\pi$
$829$	28.0757	0.975110	0.487555	+	0.873092i	$0.337889\pi$
$830$	16.9800	0.589385
$831$	46.1375	1.60049
$832$	12.7996	0.443747
$833$	−51.0402	−1.76844
$834$	−39.0068	−1.35069
$835$	15.3735	0.532023
$836$	−25.2234	−0.872369
$837$	−23.7130	−0.819641
$838$	30.7603	1.06260
$839$	−18.0586	−0.623452	−0.311726	−	0.950172i	$-0.600907\pi$
$839$	−18.0586	−0.623452	−0.311726	+	0.950172i	$0.600907\pi$
$840$	−0.695832	−0.0240085
$841$	−22.1480	−0.763724
$842$	31.6190	1.08966
$843$	−33.5369	−1.15507
$844$	71.4065	2.45791
$845$	1.19118	0.0409780
$846$	153.246	5.26871
$847$	0.564605	0.0194001
$848$	3.14997	0.108170
$849$	−28.3595	−0.973296
$850$	57.7453	1.98065
$851$	−16.9278	−0.580279
$852$	84.8390	2.90654
$853$	12.4926	0.427738	0.213869	−	0.976862i	$-0.431393\pi$
$853$	12.4926	0.427738	0.213869	+	0.976862i	$0.431393\pi$
$854$	−1.66781	−0.0570714
$855$	−23.2450	−0.794961
$856$	−16.4635	−0.562712
$857$	−56.6674	−1.93572	−0.967861	−	0.251486i	$-0.919081\pi$
$857$	−56.6674	−1.93572	−0.967861	+	0.251486i	$0.919081\pi$
$858$	−15.0663	−0.514356
$859$	15.7613	0.537769	0.268884	−	0.963172i	$-0.413345\pi$
$859$	15.7613	0.537769	0.268884	+	0.963172i	$0.413345\pi$
$860$	20.1780	0.688065
$861$	0.972263	0.0331346
$862$	−5.61042	−0.191092
$863$	−32.5158	−1.10685	−0.553426	−	0.832898i	$-0.686680\pi$
$863$	−32.5158	−1.10685	−0.553426	+	0.832898i	$0.686680\pi$
$864$	−46.7569	−1.59070
$865$	−14.7618	−0.501915
$866$	−9.57280	−0.325297
$867$	−104.525	−3.54987
$868$	−1.09386	−0.0371281
$869$	−2.83644	−0.0962195
$870$	19.8065	0.671503
$871$	0.729638	0.0247228
$872$	38.8165	1.31449
$873$	−10.1456	−0.343375
$874$	45.8217	1.54994
$875$	1.07385	0.0363026
$876$	87.2219	2.94696
$877$	−50.5255	−1.70613	−0.853063	−	0.521808i	$-0.825258\pi$
$877$	−50.5255	−1.70613	−0.853063	+	0.521808i	$0.825258\pi$
$878$	5.46792	0.184533
$879$	−31.7069	−1.06945
$880$	−4.19005	−0.141246
$881$	36.2660	1.22183	0.610916	−	0.791695i	$-0.290801\pi$
$881$	36.2660	1.22183	0.610916	+	0.791695i	$0.290801\pi$
$882$	81.4218	2.74162
$883$	6.20413	0.208786	0.104393	−	0.994536i	$-0.466710\pi$
$883$	6.20413	0.208786	0.104393	+	0.994536i	$0.466710\pi$
$884$	−20.9986	−0.706260
$885$	−23.5774	−0.792545
$886$	68.2062	2.29143
$887$	−27.8846	−0.936273	−0.468137	−	0.883656i	$-0.655074\pi$
$887$	−27.8846	−0.936273	−0.468137	+	0.883656i	$0.655074\pi$
$888$	−16.7750	−0.562933
$889$	0.430306	0.0144320
$890$	23.4881	0.787322
$891$	7.13935	0.239177
$892$	60.7893	2.03538
$893$	48.6504	1.62802
$894$	−71.0034	−2.37471
$895$	11.8708	0.396796
$896$	−1.46883	−0.0490703
$897$	16.1421	0.538969
$898$	19.3290	0.645017
$899$	9.47893	0.316140
$900$	−54.3289	−1.81096
$901$	−15.5115	−0.516762
$902$	−16.8475	−0.560962
$903$	1.78052	0.0592519
$904$	1.15780	0.0385077
$905$	−13.4258	−0.446290
$906$	−63.8968	−2.12283
$907$	28.7486	0.954583	0.477291	−	0.878745i	$-0.341619\pi$
$907$	28.7486	0.954583	0.477291	+	0.878745i	$0.341619\pi$
$908$	16.3289	0.541894
$909$	−92.5503	−3.06970
$910$	−0.276314	−0.00915972
$911$	−5.16514	−0.171129	−0.0855644	−	0.996333i	$-0.527269\pi$
$911$	−5.16514	−0.171129	−0.0855644	+	0.996333i	$0.527269\pi$
$912$	−15.7795	−0.522512
$913$	−15.3124	−0.506767
$914$	−63.3146	−2.09426
$915$	24.6388	0.814533
$916$	−20.8546	−0.689054
$917$	−1.84440	−0.0609073
$918$	105.594	3.48511
$919$	7.43055	0.245111	0.122556	−	0.992462i	$-0.460891\pi$
$919$	7.43055	0.245111	0.122556	+	0.992462i	$0.460891\pi$
$920$	−12.9184	−0.425908
$921$	−31.0054	−1.02166
$922$	28.2653	0.930869
$923$	10.2562	0.337588
$924$	2.06118	0.0678079
$925$	10.8037	0.355224
$926$	2.20802	0.0725601
$927$	99.3718	3.26380
$928$	18.6904	0.613542
$929$	−27.1034	−0.889235	−0.444618	−	0.895721i	$-0.646660\pi$
$929$	−27.1034	−0.889235	−0.444618	+	0.895721i	$0.646660\pi$
$930$	27.3999	0.898479
$931$	25.8486	0.847154
$932$	0.402182	0.0131739
$933$	−15.1327	−0.495422
$934$	62.8107	2.05523
$935$	20.6331	0.674776
$936$	10.1980	0.333331
$937$	23.8466	0.779033	0.389516	−	0.921020i	$-0.372642\pi$
$937$	23.8466	0.779033	0.389516	+	0.921020i	$0.372642\pi$
$938$	−0.169251	−0.00552624
$939$	−66.7960	−2.17981
$940$	−45.0539	−1.46950
$941$	34.7911	1.13416	0.567078	−	0.823664i	$-0.308074\pi$
$941$	34.7911	1.13416	0.567078	+	0.823664i	$0.308074\pi$
$942$	14.0564	0.457983
$943$	18.0505	0.587805
$944$	−10.2036	−0.332098
$945$	0.819475	0.0266575
$946$	−30.8531	−1.00312
$947$	37.3671	1.21427	0.607134	−	0.794599i	$-0.292319\pi$
$947$	37.3671	1.21427	0.607134	+	0.794599i	$0.292319\pi$
$948$	9.89223	0.321285
$949$	10.5443	0.342282
$950$	−29.2443	−0.948812
$951$	86.5287	2.80589
$952$	1.48289	0.0480606
$953$	60.8631	1.97155	0.985775	−	0.168068i	$-0.0537529\pi$
$953$	60.8631	1.97155	0.985775	+	0.168068i	$0.0537529\pi$
$954$	24.7447	0.801139
$955$	−18.4922	−0.598393
$956$	−50.0799	−1.61970
$957$	−17.8613	−0.577373
$958$	6.85744	0.221554
$959$	−0.828287	−0.0267468
$960$	43.8624	1.41565
$961$	−17.8870	−0.577001
$962$	−6.66134	−0.214770
$963$	44.9428	1.44826
$964$	23.4835	0.756354
$965$	2.84481	0.0915776
$966$	−3.74441	−0.120474
$967$	47.6342	1.53181	0.765907	−	0.642952i	$-0.222290\pi$
$967$	47.6342	1.53181	0.765907	+	0.642952i	$0.222290\pi$
$968$	10.3875	0.333868
$969$	77.7035	2.49620
$970$	5.05747	0.162385
$971$	−11.7342	−0.376568	−0.188284	−	0.982115i	$-0.560293\pi$
$971$	−11.7342	−0.376568	−0.188284	+	0.982115i	$0.560293\pi$
$972$	31.5882	1.01319
$973$	0.645121	0.0206816
$974$	36.5100	1.16986
$975$	−10.3022	−0.329935
$976$	10.6629	0.341312
$977$	42.9894	1.37535	0.687677	−	0.726017i	$-0.258631\pi$
$977$	42.9894	1.37535	0.687677	+	0.726017i	$0.258631\pi$
$978$	−32.2183	−1.03023
$979$	−21.1813	−0.676957
$980$	−23.9377	−0.764663
$981$	−105.963	−3.38313
$982$	86.7826	2.76934
$983$	3.78445	0.120705	0.0603526	−	0.998177i	$-0.480777\pi$
$983$	3.78445	0.120705	0.0603526	+	0.998177i	$0.480777\pi$
$984$	17.8875	0.570234
$985$	10.1618	0.323780
$986$	−42.2096	−1.34423
$987$	−3.97557	−0.126544
$988$	10.6345	0.338328
$989$	33.0561	1.05112
$990$	−32.9150	−1.04611
$991$	21.4675	0.681938	0.340969	−	0.940075i	$-0.389245\pi$
$991$	21.4675	0.681938	0.340969	+	0.940075i	$0.389245\pi$
$992$	25.8559	0.820927
$993$	−22.2673	−0.706630
$994$	−2.37909	−0.0754602
$995$	4.89674	0.155237
$996$	53.4029	1.69213
$997$	−38.0490	−1.20502	−0.602512	−	0.798110i	$-0.705833\pi$
$997$	−38.0490	−1.20502	−0.602512	+	0.798110i	$0.705833\pi$
$998$	8.08576	0.255950
$999$	19.7558	0.625046

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.17	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.17	✓	108	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20802 q^{2} -2.87685 q^{3} +2.87536 q^{4} +1.19118 q^{5} +6.35214 q^{6} -0.105056 q^{7} -1.93280 q^{8} +5.27625 q^{9} +O(q^{10})\)	\(q-2.20802 q^{2} -2.87685 q^{3} +2.87536 q^{4} +1.19118 q^{5} +6.35214 q^{6} -0.105056 q^{7} -1.93280 q^{8} +5.27625 q^{9} -2.63016 q^{10} +2.37185 q^{11} -8.27196 q^{12} -1.00000 q^{13} +0.231966 q^{14} -3.42685 q^{15} -1.48304 q^{16} +7.30297 q^{17} -11.6501 q^{18} -3.69849 q^{19} +3.42508 q^{20} +0.302230 q^{21} -5.23709 q^{22} +5.61104 q^{23} +5.56038 q^{24} -3.58108 q^{25} +2.20802 q^{26} -6.54841 q^{27} -0.302073 q^{28} +2.61763 q^{29} +7.56656 q^{30} +3.62118 q^{31} +7.14019 q^{32} -6.82345 q^{33} -16.1251 q^{34} -0.125141 q^{35} +15.1711 q^{36} -3.01688 q^{37} +8.16635 q^{38} +2.87685 q^{39} -2.30233 q^{40} +3.21696 q^{41} -0.667330 q^{42} +5.89126 q^{43} +6.81991 q^{44} +6.28498 q^{45} -12.3893 q^{46} -13.1541 q^{47} +4.26648 q^{48} -6.98896 q^{49} +7.90710 q^{50} -21.0095 q^{51} -2.87536 q^{52} -2.12400 q^{53} +14.4590 q^{54} +2.82531 q^{55} +0.203053 q^{56} +10.6400 q^{57} -5.77979 q^{58} +6.88019 q^{59} -9.85343 q^{60} -7.18991 q^{61} -7.99565 q^{62} -0.554301 q^{63} -12.7996 q^{64} -1.19118 q^{65} +15.0663 q^{66} -0.729638 q^{67} +20.9986 q^{68} -16.1421 q^{69} +0.276314 q^{70} -10.2562 q^{71} -10.1980 q^{72} -10.5443 q^{73} +6.66134 q^{74} +10.3022 q^{75} -10.6345 q^{76} -0.249177 q^{77} -6.35214 q^{78} -1.19588 q^{79} -1.76657 q^{80} +3.01003 q^{81} -7.10312 q^{82} -6.45589 q^{83} +0.869019 q^{84} +8.69918 q^{85} -13.0080 q^{86} -7.53053 q^{87} -4.58432 q^{88} -8.93028 q^{89} -13.8774 q^{90} +0.105056 q^{91} +16.1337 q^{92} -10.4176 q^{93} +29.0446 q^{94} -4.40559 q^{95} -20.5412 q^{96} -1.92287 q^{97} +15.4318 q^{98} +12.5145 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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